I did some more tests and it seems the guards help win more games (in an asymmetrical setup) when they are assigned higher values (compared to the values they had in my first tests).

Continuing with my previous method, I used a 10 x 8 board with all normal chess pieces, giving 4 extra spaces. The extra spaces are filled with the asymmetry. (Half the games in each set were guards as white and vice versa). Results including previous + new games:

So when setting the guard's value to 350, they might be superior to knights!

Now I'm doing some more tests. This time the asymmetry is [(Bishop + Knight) vs. (2 Guards)]. Since the back rank is itself non-symmetrical (within one color), I switched one side's K and Q, so starting setup is:

I.e. not clear what meaning one should attach to results that are not consistent with the value used by the engine. When you set the value to 400 this is probably more than the value of the Bishop, but it doesn't really beat the Bishops convicingly. (The error margin in 40 games is rather large, but if it is really 400 and a Bishop is 350,and you have two of them, it would be like being a Pawn ahead,and the result should have been 65%).

One possible scenario for systematic errors would be that the opponent starts to hunt the Guards with his Bishops and Knights, as he thinks it is worth more than either of those. The side with the Guards will of course try to prevent that, but with so many minors around it might not be able to do it. The result would likely be that Bishops get traded for Guards (because the player with the Guards would try to avoid trading for Knights even more, when it cannot avoid any trade). Which would then leave him with Knights against Bishops, which is a disadvantage. But a disadvantage he brought upon himself by making unsound trades. The Guards would have derived their value mainly from the opponent overestimating them, and giving his strong pieces for it. Not from anything they did themselves. In fact, the weaker they were, the more difficult it would have been for them to escape the 'trades' that in reality just sacrifice material for them.

Usually it makes little difference whether the value used by the engine is slightly above or below that of an equivalent opponent piece, because in either case one side will try toavoid the trades. But nowyoumakeit pass 6 opponent pieces in value.

I didn't realize that you had fine-tuned the value of N and B for a 10 x 8 board (Capablanca chess).

I've found that the guards help their army the most when their value is 375. At 350 and 400 their side did not win as often.

But that part of the result is confusing to me. Guards are worth about average of (knight + bishop), so this would be around 278. But to help their army win the most often they do best when their value is set to 375? So what is their optimal exchange value (to win most games)?

I notice in Capablanca chess All pieces except pawns have their values set higher than in 8x8 games. Would there be any reason to changing all my piece values to those of Capablanca chess (when testing on a 10 x 8 board)?

changing the guard's value just a little lower or higher caused their side to lose more frequently.They help their army win the most when set to 375.Most of this data is for guards playing only from black.In the case of 375, they played 50 games in each color, scoring 50.5% overall.

I'm surprised about the narrow range at where guards play their best.

Either my test is suffering from the low game quantities (test error), or the guards seem to play best only within a narrow setting for their exchange value. If the latter, when played in real games whether to exchange them or not can have a big affect on the game outcome.

vickalan wrote:But that part of the result is confusing to me. Guards are worth about average of (knight + bishop), so this would be around 278. But to help their army win the most often they do best when their value is set to 375? So what is their optimal exchange value (to win most games)?

There are two ways a piece can help the player having it win:1) By inflicting damage to the opponent because it is so powerful that the opponent cannot escape the damage, even though he tries.2) By fooling the opponent into unforced self-destruction, because he sacrifices valuable pieces to capture the piece-under-test, overrating it.

E.g. Pawns would make the side having them win most often when you set their value to 900. Because the opponent would immediately start to sacrifice his Queens, Rooks and other pieces for the Pawns. Which you cannot possibly prevent. If the opponent has no Pawns, the other side cannot make the same mistake. So when an imbalace of 6 Pawns versus a Rook you would get a 50% score (say) with P=100, you probably would score 100% with a Pawn value of 900, because the side with the Rook would sacrifice 6 more of his pieces for Pawns. But that does not mean there is any reality in a Pawn value of 900.

The game results show that the Guard is worth between N and B (so less than B), even when the opponent thinks it is worth more (and the Guards thus inspire suicidal Bishop tactics). Part of the score is undeserved, brought about by B for G trades that the B side could have easily avoided if he hadnod been deluded to think B is worth more than G. The game result obtained when you set the G value to 278 is less corrupted, because it elimiates the unnecessary Bishop sacs. But the resulting score suggests an even lower value for the Guard.

In summary: in self-play you should believe the game result, not which programmed value does best. If you want to optimize by varying the programmed value, you should do it when playing against an opponent that uses a fixed value, in a symmetric start position. E.g. it would immediately be obvious that a Pawn value of 900 is madness, when you play a standard FIDE game against an opponent that knowsit is more like 100. So you could try games where both sides have Guards, and one thinks they are worth 259, and the other thinks 350, and then measure how they fare. (You would have to make a copy of Fairy-Max for that.)

I notice in Capablanca chess All pieces except pawns have their values set higher than in 8x8 games. Would there be any reason to changing all my piece values to those of Capablanca chess (when testing on a 10 x 8 board)?

For historic reasons the values in normal Chess are lower than usual. This was because Fairy-Max was derived from micro-Max, which was developed for the goal of making the source code as small as possible. For Capablanca Chess I used a more conventional value scale.

H.G.Muller wrote:In summary: in self-play you should believe the game result, not which programmed value does best.

Ok, thanks. That's what I believed so also. I changed all the piece values to match those in Capablanca.Now the discrepancy between game results, and values used for pieces has diminished or disappeared altogether. Here's the result of 200 more games:

Also, now the results aren't so sensitive to different values for the guards. The army with the guards won 47% of games whether the guard's value was set to 330 or 375. (Black also won slightly more than white, but I assume the fist move advantage nearly goes away, because most games seemed quite long).

I think I'm happy with these results. I can probably keep running more tests for some more fine-tuning, but I don't think results will change much.

I'm currently in 3 games of chess-on-an-infinite plane. I'm beginning to feel it could use more powerful pieces to increase the tempo slightly. This is a place where monstrous pieces can exist I think. I might start testing stronger pieces on larger boards using Fairy-max.